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#1 2016-10-13 14:44:09

Sheff
Member
Registered: 2016-09-27
Posts: 4

Supremum Property of Real Number

Let S = [0,1]. If x and y are in s with x ≠y. How can we show that there are m,n∈N such that x< m/2^n <y. Can the Archimedean Property be used to prove this? If yes, could anyone provide me an insight to do this?

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#2 2016-10-23 01:29:00

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,835
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Re: Supremum Property of Real Number

Have you seen the proof of the fact that there is a rational number between any two reals?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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